Geometry Problem 1516: Finding the Length of a Side in an Equiangular Hexagon with Given Three Side Lengths. Difficulty Level: High School.

In an equiangular hexagon ABCDEF, AB = 3, BC = 7, and EF = 2. Find the measure of DE.

Geometry Problem 1516: Finding the Length of a Side in an Equiangular Hexagon with Given Three Side Lengths

Definitions and Suggestions

Geometric Shape Theorem
Equiangular Hexagon The sum of the interior angles of an equiangular hexagon is 720 degrees. Each interior angle of an equiangular hexagon measures 120 degrees.
Equilateral Triangle An equilateral triangle is also equiangular, and each of its interior angles measures 60 degrees. All three sides of an equilateral triangle are equal.
Parallel Lines The corresponding angles formed by a transversal intersecting two parallel lines are congruent. The alternate interior angles are congruent.

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Discover Even More: See Also...

Problem 1517

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Problem 1515

Geometry Problem 1515: Mastering Triangle Distance Calculation: Find the Distance from the Intersection of Medians to an Exterior Line

Problem 1514

Geometry Problem 1514: Discover the Secret to Finding Distances in Regular Hexagons with Interior Squares. Difficulty Level: High School

Problem 1513

Geometry Problem 1513: Solving the base in a Right Trapezoid with Double Angle and Sum of Two Sides. Difficulty Level: High School

Problem 1512

Geometry Problem 1512: Finding the Length of a Segment in a Triangle with a Median and a Cevian with Given Ratio. Difficulty Level: High School

Problem 1511

Geometry Problem 1511: Finding the Altitude of an Isosceles Triangle Using Distances from a Point on the Extension of the Base. Difficulty Level: High School

Thematic Poem: Finding the Length of a Side in an Equiangular Hexagon

In the realm of shapes and lines,
Geometry holds its design,
A problem to solve with great care,
Equiangular hexagon, quite rare.

With three side lengths at our behest,
We seek the length of the fourth, our quest,
Angles equal, sixty degrees,
Precision paramount, our expertise.

In the world of math and art,
Geometry sets us apart,
Solving puzzles, one by one,
Finding solutions, 'til we're done.

If you're interested in finding more poems with a focus on geometry, you may enjoy this collection: More geometry thematic poems.

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